7. Consider an experiment whose sample space consists of all positive integer (a.k.a. natural) numbers Z+ = {1,2,3,...} (i.e., we wish to choose a random natural number). (a) Can you define a probability on S = Z+? If so, then give an example and check that it is consistent with the axioms. If not, why not? (b) Can you define a probability on S = Z+ in such a way that any two numbers are equally likely to occur? If so, then give an example and check that it is consistent with the axioms. If not, why not? (c) Optional (extra credit, 2 points): Along the lines of part (b), can you define a probability on the interval S = [0, 1] in such a way that any two numbers in this interval are equally likely to occur